Differentiating with respect to x^2 and 1/(1-x)... AP review problem

**zachd77** · December 29th 2012, 04:02 PM

I'm reviewing my first semester of AP Calculus. While doing some review questions, I came across these two problems.

If , find the derivative of with respect to .
If , find the derivative of with respect to .

I started manipulating the derivative notation in order to get the solution, but how do I continue this problem?

**skeeter** · December 29th 2012, 04:57 PM

(1) $y = \sqrt{x^2+1}$

$y^2 = x^2 + 1$

$\frac{d}{dx^2}(y^2 = x^2 + 1)$

$\frac{dy^2}{dx^2}= 1$

(2) let $u = \frac{1}{1-x}$

$\frac{du}{dx} = \frac{1}{(1-x)^2}$

$y = x^2+x$

$\frac{dy}{dx} = 2x+1$

$\frac{dy}{du} = \frac{\frac{dy}{dx}}{\frac{du}{dx}} = (2x+1) \cdot (1-x)^2$

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